If Great Mathematicians Had a Signature Formula, What Would It Be?

If six of the greatest mathematicians in history could each pick one signature formula, which would it be? We take one famous formula from each of Pythagoras, Newton, Leibniz, Euler, Gauss and Ramanujan, and show where it came from, mostly in pictures. For each formula: the person, the problem, the breakthrough, and what it still does today. • Pythagoras and a² + b² = c², and a clay tablet of Pythagorean triples written more than 1,000 years before he was born • Newton and the Fundamental Theorem of Calculus: speed and area are the same question • Leibniz and the ∫ sign: the notation everyone still writes • Euler's identity, e^(iπ) + 1 = 0: why growth and rotation turn out to be one idea • Gauss and quadratic reciprocity, his "golden theorem" about prime numbers • Ramanujan's series for 1/π, about 8 more digits of pi with every term Chapters 0:00 Intro 0:42 Pythagoras: a formula older than its name 4:15 Newton: the mathematics of change 6:56 Leibniz: how we write math 9:50 Euler: the beauty of mathematics 13:08 Gauss: the secret of the primes 16:42 Ramanujan: a strange formula for pi 20:06 Putting it together 20:46 One formula each Sources MacTutor History of Mathematics (University of St Andrews), biographies of Euler, Newton, Leibniz, Gauss, Ramanujan and Pythagoras: https://mathshistory.st-andrews.ac.uk/ Wikipedia: Euler's identity; Euler's formula; Fundamental theorem of calculus; History of calculus; Leibniz's notation; Quadratic reciprocity; Srinivasa Ramanujan; Ramanujan's lost notebook; Ramanujan–Sato series; Chronology of computation of π; Pythagorean theorem; Plimpton 322; YBC 7289; Pythagoras; Thomas Heath; Fermat's Last Theorem "History of the formulas and algorithms for π": https://arxiv.org/abs/0807.0872 "Barrow and Leibniz on the fundamental theorem of the calculus": https://arxiv.org/abs/1111.6145 D. E. Joyce, Euclid's Elements, Book I, Proposition 47: https://mathcs.clarku.edu/~djoyce/ele... Linda Hall Library, "Pythagoras of Samos": https://www.lindahall.org/about/news/... Portraits Drawn in the channel's style from public-domain images on Wikimedia Commons: Euler: portrait by Jakob Emanuel Handmann, 1753 (Kunstmuseum Basel) Newton: portrait by Godfrey Kneller, 1689 Leibniz: portrait by Christoph Bernhard Francke, c. 1695 (Herzog Anton Ulrich-Museum) Gauss: portrait by Christian Albrecht Jensen, 1840 Ramanujan: seated portrait photograph, before 1920, photographer unknown (Oberwolfach Photo Collection) Pythagoras: no authentic likeness exists; drawn from a Roman bust (Capitoline Museums) made centuries after his death #math #mathhistory #calculus